Poisson: Create a Poisson distribution

Description Usage Arguments Details Value See Also Examples

View source: R/Poisson.R

Description

Poisson distributions are frequently used to model counts.

Usage

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Poisson(lambda)

Arguments

lambda

The shape parameter, which is also the mean and the variance of the distribution. Can be any positive number.

Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail.

In the following, let X be a Poisson random variable with parameter lambda = λ.

Support: {0, 1, 2, 3, ...}

Mean: λ

Variance: λ

Probability mass function (p.m.f):

P(X = k) = λ^k e^(-λ) / k!

Cumulative distribution function (c.d.f):

P(X ≤ k) = e^(-λ) ∑_{i = 0}^k λ^i / i!

Moment generating function (m.g.f):

E(e^(tX)) = e^(λ (e^t - 1))

Value

A Poisson object.

See Also

Other discrete distributions: Bernoulli(), Binomial(), Categorical(), Geometric(), HyperGeometric(), Multinomial(), NegativeBinomial()

Examples

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set.seed(27)

X <- Poisson(2)
X

random(X, 10)

pdf(X, 2)
log_pdf(X, 2)

cdf(X, 4)
quantile(X, 0.7)

cdf(X, quantile(X, 0.7))
quantile(X, cdf(X, 7))

distributions3 documentation built on Jan. 4, 2022, 1:07 a.m.